The Bohr-Weisskopf effect, or hfs anomaly, which results from the effect of the distribution of nuclear magnetization on the atomic electron-nuclear interaction, will be studied systematically first for a long chain of radioactive cesium isotopes, analogously to isotope shifts, at the PS Booster ISOLDE. Results are expected to provide an independent test for nuclear wave functions. Precision measurements of the hfs splittings and nuclear magnetic moments are required, with sensitivity adequate for the radioactive isotopes produced. A triple resonance atomic beam magnetic resonance apparatus with optical pumping state selection has been constructed. Detection of the beam is by laser induced fluorescence or mass spectrometry. The performance of the apparatus was tested with stable K and Rb beams. Results obtained for g-values and hfs anomalies are in excellent agreement with published data., and show the technique to be suitable for the on-line experiments at ISOLDE